Problem: Simplify the following expression: $r = \dfrac{5t^2 + 35t + 30}{t + 1} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ r =\dfrac{5(t^2 + 7t + 6)}{t + 1} $ Then we factor the remaining polynomial: $t^2 + {7}t + {6} $ ${1} + {6} = {7}$ ${1} \times {6} = {6}$ $ (t + {1}) (t + {6}) $ This gives us a factored expression: $\dfrac{5(t + {1}) (t + {6})}{t + 1}$ We can divide the numerator and denominator by $(t - 1)$ on condition that $t \neq -1$ Therefore $r = 5(t + 6); t \neq -1$